Rotation invariance is essential for precise, object-level segmentation in UAV aerial imagery, where targets can have arbitrary orientations and exhibit fine-scale details. Conventional segmentation architectures like U-Net rely on convolution operators that are not rotation-invariant, leading to degraded segmentation accuracy across varying viewpoints. Rotation invariance can be achieved by expanding the filter bank across multiple orientations; however, this will significantly increase computational cost and memory traffic. In this paper, we introduce a GPU-optimized rotation-invariant convolution framework that eliminates the traditional data-lowering (im2col) step required for matrix-multiplication-based convolution. By exploiting structured data sharing among symmetrically rotated filters, our method achieves multi-orientation convolution with greatly reduced memory traffic and computational redundancy. We further generalize the approach to accelerate convolution with arbitrary (non-symmetric) rotation angles. Across extensive benchmarks, the proposed convolution achieves 20--55% faster training and 15--45% lower energy consumption than CUDNN, while maintaining accuracy comparable to state-of-the-art rotation-invariant methods. In the eight-orientation setting, our approach achieves up to 45% speedup and 41% energy savings on 256\(\times\)256 inputs, and 32% speedup and 23% lower energy usage on 1024\(\times\)1024 inputs. Integrated into a U-Net segmentation model, the framework yields up to 6% improvement in accuracy over the non-rotation-aware baseline. These results demonstrate that the proposed method provides an effective and highly efficient alternative to existing rotation-invariant CNN frameworks.